2,778 research outputs found
Geodesic Transport Barriers in Jupiter's Atmosphere: A Video-Based Analysis
Jupiter's zonal jets and Great Red Spot are well known from still images. Yet
the planet's atmosphere is highly unsteady, which suggests that the actual
material transport barriers delineating its main features should be
time-dependent. Rare video footages of Jupiter's clouds provide an opportunity
to verify this expectation from optically reconstructed velocity fields.
Available videos, however, provide short-time and temporally aperiodic velocity
fields that defy classical dynamical systems analyses focused on asymptotic
features. To this end, we use here the recent theory of geodesic transport
barriers to uncover finite-time mixing barriers in the wind field extracted
from a video captured by NASA's Cassini space mission. More broadly, the
approach described here provides a systematic and frame-invariant way to
extract dynamic coherent structures from time-resolved remote observations of
unsteady continua
Fast Algorithms for Surface Reconstruction from Point Cloud
We consider constructing a surface from a given set of point cloud data. We
explore two fast algorithms to minimize the weighted minimum surface energy in
[Zhao, Osher, Merriman and Kang, Comp.Vision and Image Under., 80(3):295-319,
2000]. An approach using Semi-Implicit Method (SIM) improves the computational
efficiency through relaxation on the time-step constraint. An approach based on
Augmented Lagrangian Method (ALM) reduces the run-time via an Alternating
Direction Method of Multipliers-type algorithm, where each sub-problem is
solved efficiently. We analyze the effects of the parameters on the level-set
evolution and explore the connection between these two approaches. We present
numerical examples to validate our algorithms in terms of their accuracy and
efficiency
A Semi-Lagrangian Scheme with Radial Basis Approximation for Surface Reconstruction
We propose a Semi-Lagrangian scheme coupled with Radial Basis Function
interpolation for approximating a curvature-related level set model, which has
been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces
from sparse, possibly noisy data sets. The main advantages of the proposed
scheme are the possibility to solve the level set method on unstructured grids,
as well as to concentrate the reconstruction points in the neighbourhood of the
data set, with a consequent reduction of the computational effort. Moreover,
the scheme is explicit. Numerical tests show the accuracy and robustness of our
approach to reconstruct curves and surfaces from relatively sparse data sets.Comment: 14 pages, 26 figure
Second-order Shape Optimization for Geometric Inverse Problems in Vision
We develop a method for optimization in shape spaces, i.e., sets of surfaces
modulo re-parametrization. Unlike previously proposed gradient flows, we
achieve superlinear convergence rates through a subtle approximation of the
shape Hessian, which is generally hard to compute and suffers from a series of
degeneracies. Our analysis highlights the role of mean curvature motion in
comparison with first-order schemes: instead of surface area, our approach
penalizes deformation, either by its Dirichlet energy or total variation.
Latter regularizer sparks the development of an alternating direction method of
multipliers on triangular meshes. Therein, a conjugate-gradients solver enables
us to bypass formation of the Gaussian normal equations appearing in the course
of the overall optimization. We combine all of the aforementioned ideas in a
versatile geometric variation-regularized Levenberg-Marquardt-type method
applicable to a variety of shape functionals, depending on intrinsic properties
of the surface such as normal field and curvature as well as its embedding into
space. Promising experimental results are reported
Evaluating the structure and magnitude of the ash plume during the initial phase of the 2010 Eyjafjallajökull eruption using lidar observations and NAME simulations
The Eyjafjallajökull volcano in Iceland erupted explosively on 14 April 2010, emitting a plume of ash into the atmosphere. The ash was transported from Iceland toward Europe where mostly cloud-free skies allowed ground-based lidars at Chilbolton in England and Leipzig in Germany to estimate the mass concentration in the ash cloud as it passed overhead. The UK Met Office's Numerical Atmospheric-dispersion Modeling Environment (NAME) has been used to simulate the evolution of the ash cloud from the Eyjafjallajökull volcano during the initial phase of the ash emissions, 14–16 April 2010. NAME captures the timing and sloped structure of the ash layer observed over Leipzig, close to the central axis of the ash cloud. Relatively small errors in the ash cloud position, probably caused by the cumulative effect of errors in the driving meteorology en route, result in a timing error at distances far from the central axis of the ash cloud. Taking the timing error into account, NAME is able to capture the sloped ash layer over the UK. Comparison of the lidar observations and NAME simulations has allowed an estimation of the plume height time series to be made. It is necessary to include in the model input the large variations in plume height in order to accurately predict the ash cloud structure at long range. Quantitative comparison with the mass concentrations at Leipzig and Chilbolton suggest that around 3% of the total emitted mass is transported as far as these sites by small (<100 μm diameter) ash particles
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Investigating the ozone cycle on Mars using GCM modelling and data assimilation
Numerische Modellierung und Simulation von Kavitationsblasenwolken mit einer Lagrange-Euler-Methode
In this thesis, the Lagrangian-Eulerian coupling model is proposed to investigate dynamically the cavitation bubble cloud. Based on the Lagrangian-Eulerian one-way coupling model, the homogeneous cavitation nucleation inside microchannel is studied. Furthermore, we develop the Lagrangian-Eulerian two-way coupling for the numerical simulation of the bubble cluster with pressure wave interaction and the bubble cloud Rayleigh collapse.In dieser Doktorarbeit wird das Lagrange-Euler-Kopplungsmodell vorgeschlagen, um die Kavitationsblasenwolke dynamisch zu untersuchen. Basierend auf dem Lagrange-Euler-Einweg-Kopplungsmodell wird die homogene Kavitationskeimbildung im Mikrokanal untersucht. Darüber hinaus entwickeln wir die Lagrange-Euler-Zweiwege-Kopplung zur numerischen Simulation des Blasenclusters mit Druckwellenwechselwirkung und dem Rayleigh-Kollaps der Bubble Cloud
High-Order Unstructured Lagrangian One-Step WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems: Applications to Compressible Multi-Phase Flows
In this article we present the first better than second order accurate
unstructured Lagrangian-type one-step WENO finite volume scheme for the
solution of hyperbolic partial differential equations with non-conservative
products. The method achieves high order of accuracy in space together with
essentially non-oscillatory behavior using a nonlinear WENO reconstruction
operator on unstructured triangular meshes. High order accuracy in time is
obtained via a local Lagrangian space-time Galerkin predictor method that
evolves the spatial reconstruction polynomials in time within each element. The
final one-step finite volume scheme is derived by integration over a moving
space-time control volume, where the non-conservative products are treated by a
path-conservative approach that defines the jump terms on the element
boundaries. The entire method is formulated as an Arbitrary-Lagrangian-Eulerian
(ALE) method, where the mesh velocity can be chosen independently of the fluid
velocity.
The new scheme is applied to the full seven-equation Baer-Nunziato model of
compressible multi-phase flows in two space dimensions. The use of a Lagrangian
approach allows an excellent resolution of the solid contact and the resolution
of jumps in the volume fraction. The high order of accuracy of the scheme in
space and time is confirmed via a numerical convergence study. Finally, the
proposed method is also applied to a reduced version of the compressible
Baer-Nunziato model for the simulation of free surface water waves in moving
domains. In particular, the phenomenon of sloshing is studied in a moving water
tank and comparisons with experimental data are provided
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